∗-π-Reversible ∗-Semirings and Their Applications to Generalized Inverses

We introduce and study a new class of ∗-semirings which is called ∗-π-reversible ∗-semirings. A ∗-semiring R is said to be ∗-π-reversible if for any a,b∈R, ab=0 implies there exist two positive integers m and n such that bman∗=0. Some characterizations and examples of this class of semirings are giv...

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Bibliographic Details
Main Authors: Yuanfan Zhuo, Qinqin Gu
Format: Article
Language:English
Published: Wiley 2024-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/jom/5289722
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Summary:We introduce and study a new class of ∗-semirings which is called ∗-π-reversible ∗-semirings. A ∗-semiring R is said to be ∗-π-reversible if for any a,b∈R, ab=0 implies there exist two positive integers m and n such that bman∗=0. Some characterizations and examples of this class of semirings are given. As applications, generalized inverses related to ∗-π-reversible ∗-semirings are studied. For an additive cancellative, Id-complemented and ∗-π-reversible ∗-semiring R, if a∈R is reflexive invertible, some equivalent characterizations of a being normal elements and strong EP elements are given.
ISSN:2314-4785